Yes, but it's difficult
You'd need some sort of effect designed to put the shackles on you as soon as you left the material plane. An example of an effect with the required timing priority is Contingency. An example of an effect capable of activating the shackles on you mid-teleport is to also be wearing bracers of armor +1 or another cheap wrist slot item that counts as part of a suit of armor, yet also renders either both items or just the manacles non-functional, and then to use Instant Armor to replace said item, allowing the manacles to function.
Regardless of the method, if you do manage to equip the shackles, you do so on the Astral Plane, during your brief period there during your teleportation:
Powerful spellcasters utilize the Astral Plane for a tiny fraction of a second when they teleport
(from the planar description of the astral)
Whether or not you stay there, however, is unclear; dimensional shackles may not affect people who don them on the astral or ethereal, depending on how your DM interprets 'movement':
A dimensional anchor does not interfere with the movement of creatures already in ethereal or astral form when the spell is cast
And if you do stay there, it's very much unclear what happens to your teleportation effect.
Short answer, no.
The rules for the Dimensional Shackles indicate that they function on 'any creature bound within them'. This tends to fit the description of a Use-Activated item. No further details are given about how to bind a creature within them, so it would be a GM judgement call. Lacking any other information, I would expect these items simply work when used, fitting best the condition
If the item’s activation is subsumed in its use and takes no extra time use, activation is not an action at all
from Use Activated items.
'Shackles', as a non-magical item, are not currently defined in Pathfinder rules. The closest we get to a definition for normal shackles are probably the spell of the same name, which summons either a set of manacles or fetters - both items work similarly, but don't actually have any rules on how to actually apply them to a creature, instead simply giving mechanics for how to deal with them once on.
Another very similar item, the Thorned Manacles, outright specify that you need to apply them to an already helpless creature, but again, don't actually specify any sort of action required.
So, in summary, to apply a set of Dimensional Shackles, you need to find some way to incapacitate or restrain your target first, which is generally not possible in the middle of Spell-like Ability.
You can't interrupt a teleportation mid-execution because it is instantaneous.
It is true that there are multiple ways in which you can interrupt a character's action. For example, immediate actions, readied actions and contingent spells are all able to interrupt the flow of actions and be resolved first.
Let's suppose that Gildoragh is capable of using one of these special actions that interrupt the initiative order to put on the manacles in some way (such as bringing with him another character with a readied action).
Dimensional Steps (Sp): At 8th level, you can use this ability to teleport up to 30 feet per wizard level per day as a standard action. This teleportation must be used in 5-foot increments and such movement does not provoke an attack of opportunity. (...)
This effect is a teleportation, which is defined in the magic rules.
Teleportation: a teleportation spell transports one or more creatures or objects a great distance. The most powerful of these spells can cross planar boundaries. Unlike summoning spells, the transportation is (unless otherwise noted) one-way and not dispellable.
Teleportation is instantaneous travel through the Astral Plane. Anything that blocks astral travel also blocks teleportation.
As you can see, the teleportation part of the action is an instantaneous effect. One moment you were at one place, the next instant you were somewhere else. Since it is instantaneous, there is no "mid-action" at which point you can react.
... but you can interrupt a Dimensional Step.
While the teleportation can not be blocked while it happens, the dimensional step itself could be. Suppose that a readied action to put on the manacles has the trigger "when Gildoragh activates his dimensional step ability". When the condition is met, the readied action is triggered and resolved.
Because Gildoragh is now affected by Dimensional Anchor, the teleportation fails. In that case, Gildoragh didn't move at all and remains at the same place.